Week 6, Day 3

Attached is a link to a google site we created to help you better prepare for the chapter 8 test! I hope you find this helpful! :) 

https://sites.google.com/a/maranathastudents.org/chapter-8-group-1/

Week 6, Day 2

Today we learned four applications of matrices: 

1. How to find the area of a triangle

2. How to determine if points are collinear

3. How to identify the equation of a line

4. How to use Cramer's Rule

Here is an outline of how to perform each process.

In addition, our group has created a Voicethread, guiding you through the process of determining  the area of a triangle. It discusses the general setup and provides an example problem. 

https://voicethread.com/share/5424595

Week 6, Day 1

Today we learned how to find the determinants of matrices. Here a couple practice problems.

Attached below is a link to an Educreations video we created to explain the lesson.

http://www.educreations.com/lesson/view/determinant-of-matrices/16849898/?s=oyvDFX&ref=app

Soul Mate Prediction

Ever daydream where that special someone might be? Well, a mathematical formula has been invented to help you find this person, your soulmate. Simply follow these instructions:

1. Look at the soul mate prediction wheel above. 

2. Choose Vancouver.

3. Take the last four digits of your phone number and write them down.

4. Scramble these four digits to create a new number.

5. Subtract the smaller number from the larger number.

6. Add these four digits to obtain a total.

7. Start counting clockwise from Vancouver.

(Vancouver = 1, Tokyo = 2, Mali = 3, Dubai = 4, etc.) 

8. When you have reached your number, stop on that city.

9. Congratulations! You have found your soul mate ;) 

(My prediction was Montreal). 

Week 5, Day 2

Today we learned about inverse matrices. A^-1 is called the inverse of A.

Show that B is the inverse of A where, 

To show that B is the inverse of A, show that AB = I = BA, as follows.

If a matrix A has an inverse, A is called invertible or nonsingular; otherwise, A is called singular. A nonsquare matrix cannot have an inverse. The following are example problems demonstrating how to solve for inverse matrices (one singular and one is not). 

Week 5, Day 1

A System With No Solution:

When solving a system of linear equations, you should remember that it is possible for the system to have no solution. If, in the elimination process, you obtain a row with zeros except for the last entry, it is unnecessary to continue the elimination process. You can simply conclude that the system is inconsistent. The following is an example of a system with no solution:

x - y + 2y = 4

x + 0y + z = 6

2x - 3y + 5z = 4

3x + 2y - z = 1

Note that the third row of this matrix consists of zeros except for the last entry. This means that the original system of linear equations is inconsistent. You can see why this is true by converting back to a system of linear equations.

x - y + 2z = 4

0x + y - z = 2

0 = -2

0x + 5y - 7y = -11

Because the third equation is not possible, the system has no solution. 

A System With Infinite Solutions:

When solving a system of linear equations, it is also possible to produce an answer with infinitely many solutions. This occurs when there are two equations to solve for three variables. The following is an example of a system with an infinite number of solutions:

2x + 4y - 2z = 0

3x + 5y + 0z = 1

The corresponding system of equations is:

x + 5z = 2

y - 3z = -1

Solving for x and y in terms of z, you have x = -5z + 2 and y = 3z -1. Then, letting z = a, the solution set has the form: ( -5a + 2, 3a - 1, a) where a is a real number. Try substituting values for a to obtain a few solutions. Then check each solution in the original system of equations. 

Week 4, Day 1

Attached is a link to a prezi we created on vocabulary definitions to introduce the concept of matrices. 

In my group was Axie, Darron, and Harrison. 

http://prezi.com/poqksnaiqwz_/?utm_campaign=share&utm_medium=copy